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Area of a parallelogram

Understand why the formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.

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  • aqualine ultimate style avatar for user _:*.Big_Star_Wars_Fan.*:_
    I have 3 questions:

    1. Dose it mater if u put it like this: A= b x h or do you switch it around?

    2. Will it work for circles?

    3. How many different kinds of parallelograms does it work for?

    And may I have a upvote because I have not been getting any.
    (55 votes)
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    • blobby green style avatar for user Alatheia Hague
      It doesn't matter if u switch bxh around, because its just multiplying. When you multiply 5x7 you get 35. If you multiply 7x5 what do you get? You get the same answer, 35.

      2.There is a diffrent formula for a circle, triangle, cimi circle, it goes on and on. The formula for circle is:
      A= Pi x R squared.
      (7 votes)
  • blobby green style avatar for user Annie Ma
    1. Does it work on a quadrilaterals?
    2. Can this also be used for a circle?
    Sorry for so my useless questions :(
    (6 votes)
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  • starky ultimate style avatar for user Pablo Lopez
    What is the formula for a solid shape like cubes and pyramids?
    (7 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      Nice question!

      For 3-D solids, the amount of space inside is called the volume. Volume in 3-D is therefore analogous to area in 2-D.

      The volume of a cube is the edge length, taken to the third power. The volume of a rectangular solid (box) is length times width times height. Note that these are natural extensions of the square and rectangle area formulas, but with three numbers, instead of two numbers, multiplied together.

      The volume of a pyramid is one-third times the area of the base times the height. Note that this is similar to the area of a triangle, except that 1/2 is replaced by 1/3, and the length of the base is replaced by the area of the base.
      (1 vote)
  • aqualine ultimate style avatar for user KahWee ⚽🥇🏆🎮🕹
    What is the formula for a solid shape like cubes and pyramids
    (3 votes)
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  • boggle yellow style avatar for user andy
    What about parallelograms that are sheared to the point that the height line goes outside of the base? I can't manipulate the geometry like I can with the other ones. Would it still work in those instances?
    (3 votes)
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  • mr pants purple style avatar for user MackennaM
    then how do we get the tip of the area
    (3 votes)
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  • hopper cool style avatar for user AJ
    This video was very helpful, thank you.
    (3 votes)
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  • winston default style avatar for user Liam Kirby
    How do you do quantum mechanics
    (3 votes)
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  • piceratops sapling style avatar for user Timothy C
    I have one question:
    How do you calculate the angle degree of a dodecagon?
    (2 votes)
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  • starky ultimate style avatar for user Pablo Lopez
    How can you find area on 3-d shapes?
    (2 votes)
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    • blobby green style avatar for user HannahV
      Great question!
      For 3-Dimensional shapes there is a formula called volume, and volume is basically when you multiply Length times width times height. So you would NOT say"How can you find the area of a 3-Dimensional figure" you would say"How can you find the VOLUME of a 3-Dimensional figure".But that's something you learn a bit later in 6th grade.
      (1 vote)

Video transcript

- If we have a rectangle with base length b and height length h, we know how to figure out its area. Its area is just going to be the base, is going to be the base times the height. The base times the height. This is just a review of the area of a rectangle. Just multiply the base times the height. Now let's look at a parallelogram. And in this parallelogram, our base still has length b. And we still have a height h. So when we talk about the height, we're not talking about the length of these sides that at least the way I've drawn them, move diagonally. We're talking about if you go from this side up here, and you were to go straight down. If you were to go at a 90 degree angle. If you were to go perpendicularly straight down, you get to this side, that's going to be, that's going to be our height. So in a situation like this when you have a parallelogram, you know its base and its height, what do we think its area is going to be? So at first it might seem well this isn't as obvious as if we're dealing with a rectangle. But we can do a little visualization that I think will help. So what I'm going to do is I'm going to take a chunk of area from the left-hand side, actually this triangle on the left-hand side that helps make up the parallelogram, and then move it to the right, and then we will see something somewhat amazing. So I'm going to take this, I'm going to take this little chunk right there, Actually let me do it a little bit better. So I'm going to take that chunk right there. And let me cut, and paste it. So it's still the same parallelogram, but I'm just going to move this section of area. Remember we're just thinking about how much space is inside of the parallelogram and I'm going to take this area right over here and I'm going to move it to the right-hand side. And what just happened? What just happened? Let me see if I can move it a little bit better. What just happened when I did that? Well notice it now looks just like my previous rectangle. That just by taking some of the area, by taking some of the area from the left and moving it to the right, I have reconstructed this rectangle so they actually have the same area. The area of this parallelogram, or well it used to be this parallelogram, before I moved that triangle from the left to the right, is also going to be the base times the height. So the area here is also the area here, is also base times height. I just took this chunk of area that was over there, and I moved it to the right. So the area of a parallelogram, let me make this looking more like a parallelogram again. The area of a parallelogram is just going to be, if you have the base and the height, it's just going to be the base times the height. So the area for both of these, the area for both of these, are just base times height.